#### Basic pool math isn’t rocket science… it’s not brain surgery… but it can be complicated. Even seasoned operators find themselves stumped by seemingly basic pool math problems. Troubleshooting pool issues often starts with a bit of math – and getting that math right may make all the difference. To help, we’ve dug deep and compiled a summary of the basic pool math you need to know, with simple explanations for how the numbers impact your job.

**Surface Area and Volume** – Let’s start with the basics. Before we dose chemicals or buy pump room equipment, we’re going to need to know how big your pool is. We’ll find that both surface area and volume are tremendously useful numbers to know. Much of the later math we’ll discuss use these values.

To figure out surface area, we’ll use a couple basic formulas:

*Surface Area of a Rectangular Pool = Length x Width *

*Surface Area of a Circular Pool = Radius x Radius x 3.14*

Tip – Make sure all of your measurements are starting in linear feet, not meters or yards. Not sure how to convert? See the conversion section below.

Tip – A radius is the distance from the center of a circle to its outside edge (halfway across the circle). When sizing circles, 3.14 is a constant number in the formula, representing the number Pi.

Our volume formulas are very similar:

*Volume of a Rectangular Pool = Length x Width x Average Depth x 7.5*

*Volume of a Circular Pool = Radius x Radius x 3.14 x Average Depth x 7.5*

Tip – The number 7.5 at the end of both equations is a constant representing the amount of water in a cubic foot. If this value was not included in the formula, your answer would be given in cubic feet, as opposed to gallons.

Tip – Average depth is an easier value to determine than you may think. Simply add the deep end depth, to the shallow end depth and divide by two.

*Average Depth = (Shallow End Depth + Deep End Depth) / 2 *

Tip – Multiple sections or depths in your pool? Break it up into simple areas and repeat the math.

Tip – Have an odd shaped pool? The math for figuring out your surface area or volume may be very complex. Check your pool permit, engineering specs or blueprints. Many of these documents show your surface area and volume.

**Conversions **– Pool operators are frequently tasked with performing a mathematical conversion. Make sure you know the most common poolside conversions:

Dry Ounces to Pounds Ounces / 16 = Pounds

Fluid Ounces to Gallons Fluid Ounces / 128 = Gallons

Yards to Feet Yards x 3 = Feet

Meters to Feet Meters x 3.28 = Feet

**Chemical Adjustment** – Ready to add a chemical to your pool? You’ll need to consider three variables:

- The volume of your pool
- The desired change in chemical value, measured in parts per million (ppm)
- Chemical dosing recommendations (from the product label or an adjustment guide)

Example: You are planning to add calcium hypochlorite (dry chlorine) to your 35,000 gallon pool. You would like to raise your ppm from 2 to 5. The product label instructions note that you would add 2 ounces per 10,000 gallons of water for a 1 ppm change.

Here’s how the variables would produce factors and a final dosage:

Your Pool Recommendations Factor

**Volume ** 35,000 Gallons / 10,000 Gallons = 3.5

**Desired Change ** 3 ppm / 1 ppm = 3

**Dosage Recommendation**………………………………………………………………………… = 2 oz.

Simply multiply your three factors for your final dosage amount:

3.5 x 3 x 2 ounces = __21 ounces__

**Breakpoint Chlorination **– You can smell a poorly treated pool from a mile away. The smell associated some pools is often blamed on chlorine, but that’s not what your patrons are smelling. The smell is actually attributed to chloramines, the gaseous bi-product of combined chlorine. Although there are a few methods for chloramine reduction, one of the most effective is a chemical process known as breakpoint chlorination. Raising your chlorine levels rapidly can separate combined chlorines and dramatically improve air quality in your facility. Here’s the basic formula that helps us figure out how much chlorine we need to add to achieve breakpoint.

Total Chlorine

– __Free Chlorine__

= Combined Chlorine

X __10____________

= Breakpoint

– __Free Chlorine__

= PPM Change

Tip – This formula only needs two numbers to work, your total chlorine and your free chlorine (which is used twice in the equation). Both can be determined with a common pool test kit. Your final answer is your desired ppm adjustment and can be used in the standard chemical adjustment formula described above.

**Heating** – In the market for a new heater? They’re sized in BTU’s or British Thermal Units. Figuring out how many BTU’s your system needs uses a simple formula:

*BTU’s = Gallons x 8.33 x Change in Temperature*

Tip – Like many of our other formulas, this equation features a constant (8.33) that is used in determining BTU’s when considering a temperature change in Fahrenheit.

__Turnover__** , Volume and Flow Rate** – Pools are designed to set specifications with regards to turnover, volume and flow. Because of this, there are consistent relationships between these numbers that become useful in pool operations. These relationships can be represented in the following set of formulas.

*Turnover Rate = Volume / Flow Rate / 60*

*Flow Rate = Volume / Turnover Rate / 60** *

Tip – Because we’re moving between minutes and hours in these equations, the number 60 is included as a constant in both formulas.

Tip – Turnover rate is measured in hours, flow rate is measured in gallons per minute and volume is measured in gallons in these equations.

**Filtration** – Like turnover, volume and flow rate, our filters also follow a set of design standards that can be useful in day to day operations. These relationships yield yet another set of formulas.

*Filter Area = Flow Rate / Filter Media Rate*

*Filter Media Rate = Flow Rate / Filter Area*

*Flow Rate = Filter Area x Filter Media Rate*

Tip – Although written three different ways, these are actually the same formula. When tasked with using one of these equations to determine a value, use the one that starts with the value that you are looking for.

__Formula Summary List __

**Area and Volume **

Area of a Rectangle = Length x Width

Area of a Circle = Radius x Radius x 3.14

Volume of a Rectangle = Length x Width x Average Depth x 7.5

Volume of a Circle = Radius x Radius x 3.14 x Average Depth x 7.5

**Breakpoint Chlorination Formul**

Total Chlorine

– __Free Chlorine__

= Combined Chlorine

X __10____________

= Breakpoint

– __Free Chlorine__

= PPM Change

**Turnover, Flow and Volume Relationships**

Turnover Rate = Volume / Flow Rate / 60

Flow Rate = Volume / Turnover Rate / 60

Turnover Rate is measured in Hours

Flow Rate is measured in Gallons Per Minute (gpm)

Volume is measured in Gallons

**Filter Sizing**

Filter Area = Flow Rate / Filter Media Rate

Filter Media Rate = Flow Rate / Filter Area

Flow Rate = Filter Area x Filter Media Rate

**Gas Heater Sizing**

BTU’s = Volume x 8.33 x Change in Temperature

© 2020 Aquatic Council, LLC. All rights reserved. This proprietary information is not to be duplicated for commercial use.